The present disclosure relates generally to a control system combining extremum-seeking control (ESC) with feedforward control. ESC is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. ESC can be considered a dynamic realization of gradient searching through the use of dither signals. The gradient of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using a negative feedback loop in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system.
Applications of ESC may be limited by the speed of convergence to the optimal system output y, which is not necessarily a problem for systems with a stationary optimum. However, for systems like a heating, ventilating, and air-conditioning (HVAC) system, the optimal system output y generally changes as driving conditions (e.g., ambient temperature, load on the system) change. If the speed of convergence to the optimal system output y is slower than the dynamic response of the process being optimized, it could be problematic to track the optimum. It is desirable to have a controlling system and method that converges to the optimal system performance faster than the rate of the driving conditions changes influencing the optimum.